Markus Reinhardt

Short-term and long-term diagonalization of correlated MIMO channels with adaptive modulation

Theoretical results on MIMO capacity maximization suggest the decoupling of the MIMO channel into independent subchannels with optimum water-filling on these subchannels. Those results inspire the development of real systems that diagonalize the MIMO channel and adaptively control the modulation on each of the resulting subchannels. We study the design of a fully adaptive transmitter, where transmit filtering and adaptive modulation is controlled by short-term as well as long-term channel state information (channel correlation), where the focus is on channels with correlated fading at transmitter and receiver array. To this end, we are motivating the use of long-term channel eigenmodes by capacity-independent considerations. Simulation results confirm the potential of fully adaptive transmit processing.

A closed-form bound on correlated MIMO channel capacity

The exact calculation of the ergodic MIMO channel capacity with channel correlation is mathematically at least very challenging. Having no closed-form analytical expression available for the capacity is making it difficult to derive optimum stochastic water-filling schemes that are based on long-term channel state information (channel correlation) only. We therefore derive a closed-form tight upper bound on the ergodic capacity of correlated MIMO channels. The bound takes into account both the effects of correlation at the transmitter as well as the receiver. Furthermore, we give a recursive algorithm for its efficient calculation. Simulations demonstrate the tightness of the bound and show that a long-term water-filling scheme based on the new bound yields almost the same performance as a scheme with full short-term (instantaneous) channel state information.

Performance analysis of MIMO maximum likelihood receivers with channel correlation, colored Gaussian noise, and linear prefiltering

We present an analytical performance evaluation of a Rayleigh fading MIMO link with matrix transmit prefiltering, channel correlation at transmitter and receiver, and spatially colored Gaussian noise for arbitrary two-dimensional signal constellations based on a tight union bound of the pairwise error probabilities. Asymptotic results for the high SNR region allow a simple characterization of the correlation effects and a quantification of the SNR penalty. It is shown that the diversity level of ML detection is unaffected by fading correlation and demonstrated that the effects of transmit and receive correlation may be assessed independently with the standard simplified channel model. Prefiltering algorithms based on long-term stable channel correlation characteristics are derived using the framework at hand. Simulations results illustrate the effectiveness of transmit prefilter designs based on the performance bound.

Statistical prefiltering for MMSE and ML receivers with correlated MIMO channels

The performance of wireless MIMO systems is known to suffer significantly from fading correlation between the antenna elements in a poor scattering environment if the transmitter is non-adaptive. However, acquiring accurate short-term channel state information to control TX adaptivity can be serious problem, in particular in FDD systems. Thus, we are proposing statistical linear transmit prefiltering schemes for MMSE and ML detection in the receiver that are solely based on long-term channel state information. It is demonstrated that long-term channel state information. It is demonstrated that long-term adaptive prefiltering can achieve a significant gain over non-adaptive (blind) transmission. Prefiltering for ML detection in a strongly correlated channel is shown to yield almost the same performance as the blind scheme in an uncorrelated channel. Moreover, exploiting long-term properties of the channel is especially appealing in terms of computational complexity and channel estimation, as the long-term channel estimation process can be carried out in a wide time window.

Ergodic capacity of MIMO channels with statistical channel state information at the transmitter

It is well known that with the availability of statistical channel state information at the transmitter, the capacity-achieving transmission strategy is transmission on the long-term eigen-modes of the transmit correlation matrix with adequate power allocation. However, the optimum power allocation strategy is not known in general. Using recent analytical results on mean mutual information of MIMO channels with transmit as well as receive correlation, We study the behavior of the capacity-achieving power allocation strategy. To this end, we also make use of asymptotical results for a large number of transmit or receive antennas and the high as well as low SNR regime, which in certain cases allows for a closed-form analysis. Furthermore, we investigate two low complexity power allocation schemes, which are based on certain upper bounds on mean mutual information.

Statistical prefiltering for MIMO systems with linear receivers in the presence of transmit correlation

Fading correlation at the transmit antenna array of MIMO systems causes significant performance degradation, especially in case of non-adaptive transmitters and linear receivers. We propose statistical transmit matrix prefiltering schemes for zero forcing and minimum mean squared error receivers that are controlled by knowledge of the transmit correlation matrix only, thus avoiding the need for instantaneous channel state information at the transmitter. To this end, closed-form approximations are derived for average error probability and average mean squared error, respectively, under a flat Rayleigh fading channel assumption. Based on these results, the optimum linear matrix prefilters are derived for a well-known MIMO channel model. Monte-Carlo simulations demonstrate the effectiveness of the proposed statistical prefilters.

Transformation Methods, Coding and Equalization for Time- and Frequency-Selective Channels

A method to generate transmit signal sets is proposed which are especially suited for transmission over Rayleigh fading channels. It is shown that this method in combination with a suitable iterative receive algorithm allows the asymptotical transformation of a Rayleigh channel into a set of parallel additive white gaussian noise (AWGN) subchannels. Therefore, coding methods designed for the AWGN channel are now applicable also to Rayleigh channels resulting in a coding gain that is separable into the known AWGN coding gain and an additional diversity gain attributable to the orthonormal transform. Starting from this result, the method is extended to a transmission over frequency and/or time-selective channels. This leads to an extension of the recently introduced multicamer code division multiplexing (MC-CDM) scheme. A unified transmission model is derived which allows the application of the iterative reception algorithm also in the latter case and to transform time- and frequency-selective channels under certain assumptions asymptotically into a set of parallel AWGN subchannels. The performance of these transformation methods for an uncoded scheme and together with high rate trellis codes designed for the AWGN channel is investigated and compared to the matched filter bound (MFB). For the calculation of the MFB for channels with a separable time-variant transfer function a method is introduced that significantly reduces the complexity of computation.

Cross polarisation based extension of closed loop transmit diversity

An extension to Release99 closed loop transmit diversity is proposed by combining uplink based beamforming and polarisation diversity. A generic expression for the polarisation covariance matrix is derived based on the assumption of uncorrelated fading processes for different polarisation states. It becomes evident that the product of the open loop beamforming gain and the two antenna polarisation covariance matrix gives the overall covariance matrix for the proposed transmitter structure. Specialising to 2M/spl plusmn/45/spl deg/ cross polarised transmit antennas it is shown that the overall covariance matrix shows partly correlated fading depending on the cross polarisation discrimination (XPD) and the receive antenna orientation. Simulation results for a system with eight transmit antennas show gains of 7 dB in terms of required transmit power in highly spatially correlated scenarios compared to a spatial diversity based system with two transmit antennas using space-time codes.